\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\]

↓

\[\mathsf{fma}\left(4, \frac{x}{y}, 2 - 4 \cdot \frac{z}{y}\right)\]

1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}

↓

\mathsf{fma}\left(4, \frac{x}{y}, 2 - 4 \cdot \frac{z}{y}\right)

double f(double x, double y, double z) {
        double r266996 = 1.0;
        double r266997 = 4.0;
        double r266998 = x;
        double r266999 = y;
        double r267000 = 0.25;
        double r267001 = r266999 * r267000;
        double r267002 = r266998 + r267001;
        double r267003 = z;
        double r267004 = r267002 - r267003;
        double r267005 = r266997 * r267004;
        double r267006 = r267005 / r266999;
        double r267007 = r266996 + r267006;
        return r267007;
}

↓

double f(double x, double y, double z) {
        double r267008 = 4.0;
        double r267009 = x;
        double r267010 = y;
        double r267011 = r267009 / r267010;
        double r267012 = 2.0;
        double r267013 = z;
        double r267014 = r267013 / r267010;
        double r267015 = r267008 * r267014;
        double r267016 = r267012 - r267015;
        double r267017 = fma(r267008, r267011, r267016);
        return r267017;
}

Derivation

Initial program 0.1
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\]
Taylor expanded around 0 0.0
\[\leadsto \color{blue}{\left(4 \cdot \frac{x}{y} + 2\right) - 4 \cdot \frac{z}{y}}\]
Simplified0.0
\[\leadsto \color{blue}{\mathsf{fma}\left(4, \frac{x}{y}, 2 - 4 \cdot \frac{z}{y}\right)}\]
Final simplification0.0
\[\leadsto \mathsf{fma}\left(4, \frac{x}{y}, 2 - 4 \cdot \frac{z}{y}\right)\]

Reproduce

herbie shell --seed 2019353 +o rules:numerics
(FPCore (x y z)
  :name "Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, C"
  :precision binary64
  (+ 1 (/ (* 4 (- (+ x (* y 0.25)) z)) y)))

Error

Derivation

Reproduce